Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H

Percentage Accurate: 100.0% → 100.0%

Time: 4.3s

Alternatives: 9

Speedup: 1.0×

• 20.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x + y\right) \cdot \left(1 - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (1.0d0 - z)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Python

def code(x, y, z):
	return (x + y) * (1.0 - z)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (1.0 - z);
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) \cdot \left(1 - z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (+ x y) (- 1.0 z)))

C

double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x + y) * (1.0d0 - z)
end function

Java

public static double code(double x, double y, double z) {
	return (x + y) * (1.0 - z);
}

Python

def code(x, y, z):
	return (x + y) * (1.0 - z)

Julia

function code(x, y, z)
	return Float64(Float64(x + y) * Float64(1.0 - z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x + y) * (1.0 - z);
end

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - z\right) \cdot \left(x + y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (- 1.0 z) (+ x y)))

C

double code(double x, double y, double z) {
	return (1.0 - z) * (x + y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (1.0d0 - z) * (x + y)
end function

Java

public static double code(double x, double y, double z) {
	return (1.0 - z) * (x + y);
}

Python

def code(x, y, z):
	return (1.0 - z) * (x + y)

Julia

function code(x, y, z)
	return Float64(Float64(1.0 - z) * Float64(x + y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (1.0 - z) * (x + y);
end

Wolfram

code[x_, y_, z_] := N[(N[(1.0 - z), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]

2. Final simplification 100.0%

   \[\leadsto \left(1 - z\right) \cdot \left(x + y\right) \]

Alternative 2: 76.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -1 \cdot 10^{+33}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;1 - z \leq -100 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (- 1.0 z) -1e+33)
   (* z (- y))
   (if (or (<= (- 1.0 z) -100.0) (not (<= (- 1.0 z) 2.0)))
     (* x (- 1.0 z))
     (+ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((1.0 - z) <= -1e+33) {
		tmp = z * -y;
	} else if (((1.0 - z) <= -100.0) || !((1.0 - z) <= 2.0)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((1.0d0 - z) <= (-1d+33)) then
        tmp = z * -y
    else if (((1.0d0 - z) <= (-100.0d0)) .or. (.not. ((1.0d0 - z) <= 2.0d0))) then
        tmp = x * (1.0d0 - z)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((1.0 - z) <= -1e+33) {
		tmp = z * -y;
	} else if (((1.0 - z) <= -100.0) || !((1.0 - z) <= 2.0)) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (1.0 - z) <= -1e+33:
		tmp = z * -y
	elif ((1.0 - z) <= -100.0) or not ((1.0 - z) <= 2.0):
		tmp = x * (1.0 - z)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(1.0 - z) <= -1e+33)
		tmp = Float64(z * Float64(-y));
	elseif ((Float64(1.0 - z) <= -100.0) || !(Float64(1.0 - z) <= 2.0))
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((1.0 - z) <= -1e+33)
		tmp = z * -y;
	elseif (((1.0 - z) <= -100.0) || ~(((1.0 - z) <= 2.0)))
		tmp = x * (1.0 - z);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(1.0 - z), $MachinePrecision], -1e+33], N[(z * (-y)), $MachinePrecision], If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], -100.0], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0]], $MachinePrecision]], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 1 z) < -9.9999999999999995e32

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(1 - z\right) \cdot \left(x + y\right)} \]

      2. +-commutative 100.0%

         \[\leadsto \left(1 - z\right) \cdot \color{blue}{\left(y + x\right)} \]

      3. distribute-lft-in 96.6%

         \[\leadsto \color{blue}{\left(1 - z\right) \cdot y + \left(1 - z\right) \cdot x} \]

   3. Applied egg-rr 96.6%

      \[\leadsto \color{blue}{\left(1 - z\right) \cdot y + \left(1 - z\right) \cdot x} \]

   4. Taylor expanded in z around inf 96.6%

      \[\leadsto \left(1 - z\right) \cdot y + \color{blue}{-1 \cdot \left(z \cdot x\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 96.6%

         \[\leadsto \left(1 - z\right) \cdot y + \color{blue}{\left(-1 \cdot z\right) \cdot x} \]

      2. mul-1-neg 96.6%

         \[\leadsto \left(1 - z\right) \cdot y + \color{blue}{\left(-z\right)} \cdot x \]

   6. Simplified 96.6%

      \[\leadsto \left(1 - z\right) \cdot y + \color{blue}{\left(-z\right) \cdot x} \]

   7. Taylor expanded in z around inf 96.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} + \left(-z\right) \cdot x \]
   8. Step-by-step derivation

      1. associate-*r* 96.6%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot z} + \left(-z\right) \cdot x \]

      2. neg-mul-1 96.6%

         \[\leadsto \color{blue}{\left(-y\right)} \cdot z + \left(-z\right) \cdot x \]

   9. Simplified 96.6%

      \[\leadsto \color{blue}{\left(-y\right) \cdot z} + \left(-z\right) \cdot x \]

   10. Taylor expanded in y around inf 64.6%

       \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 64.6%

          \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot z} \]

       2. mul-1-neg 64.6%

          \[\leadsto \color{blue}{\left(-y\right)} \cdot z \]

   12. Simplified 64.6%

       \[\leadsto \color{blue}{\left(-y\right) \cdot z} \]

   if -9.9999999999999995e32 < (-.f64 1 z) < -100 or 2 < (-.f64 1 z)

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in x around inf 56.6%

      \[\leadsto \color{blue}{\left(1 - z\right) \cdot x} \]

   if -100 < (-.f64 1 z) < 2

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in z around 0 98.4%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -1 \cdot 10^{+33}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;1 - z \leq -100 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 98.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - z \leq -100 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (- 1.0 z) -100.0) (not (<= (- 1.0 z) 2.0)))
   (* z (- (- y) x))
   (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -100.0) || !((1.0 - z) <= 2.0)) {
		tmp = z * (-y - x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((1.0d0 - z) <= (-100.0d0)) .or. (.not. ((1.0d0 - z) <= 2.0d0))) then
        tmp = z * (-y - x)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - z) <= -100.0) || !((1.0 - z) <= 2.0)) {
		tmp = z * (-y - x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - z) <= -100.0) or not ((1.0 - z) <= 2.0):
		tmp = z * (-y - x)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(1.0 - z) <= -100.0) || !(Float64(1.0 - z) <= 2.0))
		tmp = Float64(z * Float64(Float64(-y) - x));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - z) <= -100.0) || ~(((1.0 - z) <= 2.0)))
		tmp = z * (-y - x);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(1.0 - z), $MachinePrecision], -100.0], N[Not[LessEqual[N[(1.0 - z), $MachinePrecision], 2.0]], $MachinePrecision]], N[(z * N[((-y) - x), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 1 z) < -100 or 2 < (-.f64 1 z)

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in z around inf 98.1%

      \[\leadsto \color{blue}{-1 \cdot \left(\left(y + x\right) \cdot z\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 98.1%

         \[\leadsto \color{blue}{-\left(y + x\right) \cdot z} \]

      2. +-commutative 98.1%

         \[\leadsto -\color{blue}{\left(x + y\right)} \cdot z \]

      3. distribute-rgt-neg-out 98.1%

         \[\leadsto \color{blue}{\left(x + y\right) \cdot \left(-z\right)} \]

      4. +-commutative 98.1%

         \[\leadsto \color{blue}{\left(y + x\right)} \cdot \left(-z\right) \]

   4. Simplified 98.1%

      \[\leadsto \color{blue}{\left(y + x\right) \cdot \left(-z\right)} \]

   if -100 < (-.f64 1 z) < 2

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in z around 0 98.4%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - z \leq -100 \lor \neg \left(1 - z \leq 2\right):\\ \;\;\;\;z \cdot \left(\left(-y\right) - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 75.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := z \cdot \left(-y\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+173}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -10:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))) (t_1 (* z (- y))))
   (if (<= z -7.5e+173)
     t_0
     (if (<= z -1.7e+141)
       t_1
       (if (<= z -10.0) t_0 (if (<= z 1.0) (+ x y) t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = z * -y;
	double tmp;
	if (z <= -7.5e+173) {
		tmp = t_0;
	} else if (z <= -1.7e+141) {
		tmp = t_1;
	} else if (z <= -10.0) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * -z
    t_1 = z * -y
    if (z <= (-7.5d+173)) then
        tmp = t_0
    else if (z <= (-1.7d+141)) then
        tmp = t_1
    else if (z <= (-10.0d0)) then
        tmp = t_0
    else if (z <= 1.0d0) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = z * -y;
	double tmp;
	if (z <= -7.5e+173) {
		tmp = t_0;
	} else if (z <= -1.7e+141) {
		tmp = t_1;
	} else if (z <= -10.0) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	t_1 = z * -y
	tmp = 0
	if z <= -7.5e+173:
		tmp = t_0
	elif z <= -1.7e+141:
		tmp = t_1
	elif z <= -10.0:
		tmp = t_0
	elif z <= 1.0:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	t_1 = Float64(z * Float64(-y))
	tmp = 0.0
	if (z <= -7.5e+173)
		tmp = t_0;
	elseif (z <= -1.7e+141)
		tmp = t_1;
	elseif (z <= -10.0)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	t_1 = z * -y;
	tmp = 0.0;
	if (z <= -7.5e+173)
		tmp = t_0;
	elseif (z <= -1.7e+141)
		tmp = t_1;
	elseif (z <= -10.0)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(z * (-y)), $MachinePrecision]}, If[LessEqual[z, -7.5e+173], t$95$0, If[LessEqual[z, -1.7e+141], t$95$1, If[LessEqual[z, -10.0], t$95$0, If[LessEqual[z, 1.0], N[(x + y), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5e173 or -1.6999999999999999e141 < z < -10

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in x around inf 61.6%

      \[\leadsto \color{blue}{\left(1 - z\right) \cdot x} \]

   3. Taylor expanded in z around inf 61.6%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot x\right)} \]
   4. Step-by-step derivation

      1. associate-*r* 92.4%

         \[\leadsto \left(1 - z\right) \cdot y + \color{blue}{\left(-1 \cdot z\right) \cdot x} \]

      2. mul-1-neg 92.4%

         \[\leadsto \left(1 - z\right) \cdot y + \color{blue}{\left(-z\right)} \cdot x \]

   5. Simplified 61.6%

      \[\leadsto \color{blue}{\left(-z\right) \cdot x} \]

   if -7.5e173 < z < -1.6999999999999999e141 or 1 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(1 - z\right) \cdot \left(x + y\right)} \]

      2. +-commutative 100.0%

         \[\leadsto \left(1 - z\right) \cdot \color{blue}{\left(y + x\right)} \]

      3. distribute-lft-in 97.4%

         \[\leadsto \color{blue}{\left(1 - z\right) \cdot y + \left(1 - z\right) \cdot x} \]

   3. Applied egg-rr 97.4%

      \[\leadsto \color{blue}{\left(1 - z\right) \cdot y + \left(1 - z\right) \cdot x} \]

   4. Taylor expanded in z around inf 97.2%

      \[\leadsto \left(1 - z\right) \cdot y + \color{blue}{-1 \cdot \left(z \cdot x\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 97.2%

         \[\leadsto \left(1 - z\right) \cdot y + \color{blue}{\left(-1 \cdot z\right) \cdot x} \]

      2. mul-1-neg 97.2%

         \[\leadsto \left(1 - z\right) \cdot y + \color{blue}{\left(-z\right)} \cdot x \]

   6. Simplified 97.2%

      \[\leadsto \left(1 - z\right) \cdot y + \color{blue}{\left(-z\right) \cdot x} \]

   7. Taylor expanded in z around inf 94.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} + \left(-z\right) \cdot x \]
   8. Step-by-step derivation

      1. associate-*r* 94.9%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot z} + \left(-z\right) \cdot x \]

      2. neg-mul-1 94.9%

         \[\leadsto \color{blue}{\left(-y\right)} \cdot z + \left(-z\right) \cdot x \]

   9. Simplified 94.9%

      \[\leadsto \color{blue}{\left(-y\right) \cdot z} + \left(-z\right) \cdot x \]

   10. Taylor expanded in y around inf 61.7%

       \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 61.7%

          \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot z} \]

       2. mul-1-neg 61.7%

          \[\leadsto \color{blue}{\left(-y\right)} \cdot z \]

   12. Simplified 61.7%

       \[\leadsto \color{blue}{\left(-y\right) \cdot z} \]

   if -10 < z < 1

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in z around 0 98.4%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+173}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+141}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq -10:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]

Alternative 5: 75.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -12000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -12000.0) (not (<= z 1.0))) (* z (- y)) (+ x y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -12000.0) || !(z <= 1.0)) {
		tmp = z * -y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-12000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * -y
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -12000.0) || !(z <= 1.0)) {
		tmp = z * -y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -12000.0) or not (z <= 1.0):
		tmp = z * -y
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -12000.0) || !(z <= 1.0))
		tmp = Float64(z * Float64(-y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -12000.0) || ~((z <= 1.0)))
		tmp = z * -y;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -12000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * (-y)), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -12000 or 1 < z

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(1 - z\right) \cdot \left(x + y\right)} \]

      2. +-commutative 100.0%

         \[\leadsto \left(1 - z\right) \cdot \color{blue}{\left(y + x\right)} \]

      3. distribute-lft-in 95.3%

         \[\leadsto \color{blue}{\left(1 - z\right) \cdot y + \left(1 - z\right) \cdot x} \]

   3. Applied egg-rr 95.3%

      \[\leadsto \color{blue}{\left(1 - z\right) \cdot y + \left(1 - z\right) \cdot x} \]

   4. Taylor expanded in z around inf 95.2%

      \[\leadsto \left(1 - z\right) \cdot y + \color{blue}{-1 \cdot \left(z \cdot x\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 95.2%

         \[\leadsto \left(1 - z\right) \cdot y + \color{blue}{\left(-1 \cdot z\right) \cdot x} \]

      2. mul-1-neg 95.2%

         \[\leadsto \left(1 - z\right) \cdot y + \color{blue}{\left(-z\right)} \cdot x \]

   6. Simplified 95.2%

      \[\leadsto \left(1 - z\right) \cdot y + \color{blue}{\left(-z\right) \cdot x} \]

   7. Taylor expanded in z around inf 93.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} + \left(-z\right) \cdot x \]
   8. Step-by-step derivation

      1. associate-*r* 93.9%

         \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot z} + \left(-z\right) \cdot x \]

      2. neg-mul-1 93.9%

         \[\leadsto \color{blue}{\left(-y\right)} \cdot z + \left(-z\right) \cdot x \]

   9. Simplified 93.9%

      \[\leadsto \color{blue}{\left(-y\right) \cdot z} + \left(-z\right) \cdot x \]

   10. Taylor expanded in y around inf 55.3%

       \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   11. Step-by-step derivation

       1. associate-*r* 55.3%

          \[\leadsto \color{blue}{\left(-1 \cdot y\right) \cdot z} \]

       2. mul-1-neg 55.3%

          \[\leadsto \color{blue}{\left(-y\right)} \cdot z \]

   12. Simplified 55.3%

       \[\leadsto \color{blue}{\left(-y\right) \cdot z} \]

   if -12000 < z < 1

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in z around 0 97.8%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -12000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 6: 63.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.2e-57) (* x (- 1.0 z)) (- y (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.2e-57) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y - (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-4.2d-57)) then
        tmp = x * (1.0d0 - z)
    else
        tmp = y - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.2e-57) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.2e-57:
		tmp = x * (1.0 - z)
	else:
		tmp = y - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.2e-57)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(y - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.2e-57)
		tmp = x * (1.0 - z);
	else
		tmp = y - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.2e-57], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.1999999999999999e-57

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in x around inf 75.1%

      \[\leadsto \color{blue}{\left(1 - z\right) \cdot x} \]

   if -4.1999999999999999e-57 < x

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in x around 0 59.5%

      \[\leadsto \color{blue}{y \cdot \left(1 - z\right)} \]
   3. Step-by-step derivation

      1. sub-neg 59.5%

         \[\leadsto y \cdot \color{blue}{\left(1 + \left(-z\right)\right)} \]

      2. distribute-lft-in 59.5%

         \[\leadsto \color{blue}{y \cdot 1 + y \cdot \left(-z\right)} \]

      3. distribute-rgt-neg-out 59.5%

         \[\leadsto y \cdot 1 + \color{blue}{\left(-y \cdot z\right)} \]

      4. unsub-neg 59.5%

         \[\leadsto \color{blue}{y \cdot 1 - y \cdot z} \]

      5. *-rgt-identity 59.5%

         \[\leadsto \color{blue}{y} - y \cdot z \]

   4. Simplified 59.5%

      \[\leadsto \color{blue}{y - y \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-57}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot z\\ \end{array} \]

Alternative 7: 31.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.4 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 5.4e-142) x y))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.4e-142) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 5.4d-142) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.4e-142) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 5.4e-142:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 5.4e-142)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 5.4e-142)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 5.4e-142], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 5.3999999999999996e-142

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]

   2. Taylor expanded in x around inf 62.0%

      \[\leadsto \color{blue}{\left(1 - z\right) \cdot x} \]

   3. Taylor expanded in z around 0 36.4%

      \[\leadsto \color{blue}{x} \]

   if 5.3999999999999996e-142 < y

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot \left(1 - z\right) \]
   2. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto \color{blue}{\left(1 - z\right) \cdot \left(x + y\right)} \]

      2. +-commutative 100.0%

         \[\leadsto \left(1 - z\right) \cdot \color{blue}{\left(y + x\right)} \]

      3. distribute-lft-in 97.8%

         \[\leadsto \color{blue}{\left(1 - z\right) \cdot y + \left(1 - z\right) \cdot x} \]

   3. Applied egg-rr 97.8%

      \[\leadsto \color{blue}{\left(1 - z\right) \cdot y + \left(1 - z\right) \cdot x} \]

   4. Taylor expanded in z around inf 79.0%

      \[\leadsto \left(1 - z\right) \cdot y + \color{blue}{-1 \cdot \left(z \cdot x\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 79.0%

         \[\leadsto \left(1 - z\right) \cdot y + \color{blue}{\left(-1 \cdot z\right) \cdot x} \]

      2. mul-1-neg 79.0%

         \[\leadsto \left(1 - z\right) \cdot y + \color{blue}{\left(-z\right)} \cdot x \]

   6. Simplified 79.0%

      \[\leadsto \left(1 - z\right) \cdot y + \color{blue}{\left(-z\right) \cdot x} \]

   7. Taylor expanded in z around 0 25.0%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.4 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 8: 52.2% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ x + y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x y))

C

double code(double x, double y, double z) {
	return x + y;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + y
end function

Java

public static double code(double x, double y, double z) {
	return x + y;
}

Python

def code(x, y, z):
	return x + y

Julia

function code(x, y, z)
	return Float64(x + y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + y;
end

Wolfram

code[x_, y_, z_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]

2. Taylor expanded in z around 0 50.6%

   \[\leadsto \color{blue}{y + x} \]

3. Final simplification 50.6%

   \[\leadsto x + y \]

Alternative 9: 26.8% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot \left(1 - z\right) \]

2. Taylor expanded in x around inf 53.9%

   \[\leadsto \color{blue}{\left(1 - z\right) \cdot x} \]

3. Taylor expanded in z around 0 30.7%

   \[\leadsto \color{blue}{x} \]

4. Final simplification 30.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023224 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, H"
  :precision binary64
  (* (+ x y) (- 1.0 z)))